Correspondence: Fine Points of Filter Theory
April 1962 Radio-Electronics

April 1962 Radio-Electronics [Table of Contents] Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Electronics, published 1930-1988. All copyrights hereby acknowledged.

Sometimes one of the most interesting parts of a magazine is the Letters to the Editor. Most of the time it is composed of notes of appreciation for publishing a certain article, or appreciation for the works overall. Occasionally, a reader will sound off with a criticism of an article - some more polite than others. The magazine editor will usually give the author a chance to respond immediately after the challenge to content veracity. Such was the case in the March 1967 issue of Radio-Electronics magazine when a Zenith company engineer wrote to correct a previous article's claim regarding linear phase filter design in FM radio systems. Author Crowhusrt happened to mention in an AM-to-FM converter circuit that a Zenith scheme might not be the best approach for the application (versus a General Electric scheme). Zenith's Huenemann meant to set the record straight, but Mr. Crowhust did an admirable job defending his writing. The filter type was Bode, based on a 1935 technical paper published by Bell Telephone Company. Nerd wars.

Correspondence: Fine Points of Filter Theory

Dear Editor:

Apparently in his week of intensive work on stereo (see "Does FM Stereo Follow Its Own Theory," Radio-Electronics, October 1961, page 59), Mr. Crowhurst missed some of the fine points of modern filter theory. It is true that a linear phase (the designation "constant delay" is more descriptive) high-pass filter can be realized only with an infinitely long network. However, as Bode and Dietzold pointed out in the Bell System Technical Journal for April 1935, it is possible to approximate the constant-delay characteristic to an arbitrarily high frequency with arbitrary accuracy by using a suitably large number of critical frequencies. No filter, high pass or otherwise, has ever had a phase "advance." Furthermore, low- and high-pass Bode filters are not complementary networks. It is true that minimum-phase high-pass filters have a decreasing frequency, but a fundamental characteristic of the class of networks investigated by Bode is that they are not minimum phase. In any case, it is possible to synthesize the bandpass filter with other combinations, i.e., two low-pass filters of equal delay but differing cutoff frequencies. In fact, a direct design approach which includes no assumptions about percentage bandwidth was demonstrated by Bode. Thus the comments of Mr. Crowhurst on high-pass filters and low passband pass analogies are at best irrelevant.

Robert G. Huenemann

Zenith Radio Corp.

Chicago, Ill.

***

Dear Editor:

Mr. Huenemann's letter raises several points which would require quite an engineering treatise to answer in full. I must content myself with answering those things which are more basic to the concepts involved.

Agreed that constant delay is more descriptive than linear phase; I also realize a signal cannot arrive at the output of a filter before it is presented at the input, This does not preclude the possibility - in fact the inherent nature of high-pass filters - of producing phase advance, which is a different thing.

A transmission analogy will illustrate this distinction: A coax cable has a high-frequency cutoff, determined by its physical constants. On the other hand, a waveguide has a low cutoff frequency and is thus comparable to a high-pass filter.

Three velocities are associated with a waveguide - group velocity, phase velocity and free transmission velocity. The last-named is the velocity of propagation of electromagnetic waves in the medium contained in the guide - normally the velocity of light. Group velocity is lower and phase velocity higher than free transmission velocity.

A given bunch of energy transmitted by the frequency in question in this waveguide is delayed, but the phase of waves transmitting the energy is progressively advanced, relative to transmission in free space. Waveguide lenses utilize this fact. The waves do not leave before they enter, but they do appear to travel faster than their normal velocity.

A similar thing happens in a high-pass filter and equivalent actions. Take a simple crossover. If an input sine wave of crossover frequency is divided across an inductance and a capacitance with resistance terminations, the voltage across the capacitance is behind the input voltage in phase, while that across the inductance is correspondingly advanced. Successively more complicated crossovers increase the amount of delay and advance in complementary fashion.

We are quite aware of the varied approaches to filter design. We have also examined many multiplex adapter circuits, using filters which, from the values shown, were obviously designed from classic transmission-line-derived data which assume matching termination at input and output. These filters are then fed from a cathode follower and loaded with almost open circuit, which completely invalidates their predicted performance, in both magnitude and phase. Small wonder they don't perform to spec!

May I emphasize what the original article pointed out - the Bode filter in the Zenith publication is a low-pass configuration, not bandpass. My criticism was directed at high-pass and bandpass types, within practically realizable possibilities. The simple low-pass configurations come close to phase-linear, and the Zenith circuit, critically adjusted, should come very close indeed.

Norman H. Crowhurst

Audio Design Service

New York, N. Y.

Here is the excerpt from Mr. Crowhurst's article in dispute:

Bandpass Filters

... That criticism concerned the Zenith approach. To keep things fair, this one concerns the G -E approach! Their original design uses a bandpass filter to separate subcarrier modulation from L + R. They prescribe "phase-linear" filters for this and the associated low-pass filter.

It was only when we tried to design a phase-linear bandpass filter to the required specification that we found out there is no such animal - in this bandwidth. To "prove" that such a filter is possible, some have quoted the complicated Bode filter shown in the Zenith schematic (top of page). That is not a bandpass filter, but a low -pass type.

A phase-linear low -pass filter is no great problem. But a phase -linear high - pass cannot possibly exist, and a band - pass of this bandwidth is essentially a synthesis of the two. In a correctly designed low-pass filter, the phase delay, up to cutoff, is proportional to frequency (Fig. 5). If it's 30° at 5,000 cycles (5 kc), 60° at 10 kc, and 90° at 15 kc (all practical figures), it is phase- linear. The delay is 14 of a 15-kc cycle, 1/6 of a 10-kc cycle, or 1/12 of a 5-kc cycle, each of which means 16% microseconds, the same constant delay time.

But in a complementary high -pass filter, 90° phase advance (not delay in high pass) at 15 kc would correspond with 60° advance at 22.5 kc and 30° advance at 45 kc. These figures convert to time advances of 16.7, 7.4 and 3.3 microseconds, respectively. Nothing can be done, over a band this wide, to make the time-delay/advance characteristic anywhere near linear.

In relatively narrow bandwidth filters, where the response is due to the relative Q and coupling factor of tuned circuits, the overall response can be analyzed, to a close approximation, as analogous to a low-pass filter, where the cutoff frequency is equal to the deviation of either cutoff in the bandpass from mid-frequency (Fig. 6).

This close approximation depends on the upper cutoff being at an equal frequency fraction from mid-band with the lower cutoff. In an FM if coil, the mid-frequency is around 10 mc, and the cutoffs are a small fraction of 1 mc on either side. In a receiver for the Subsidiary Communications Authorization subcarrier multiplex, the mid-frequency is 67 kc, and the cutoffs are at 60 and 75 kc, only 6 or 7 kc above and below 67 kc - still a 10-to-1 ratio. But in the stereo subcarrier, the mid-frequency is 38 kc and the cutoffs are 23 and 53 kc, which is a very different kettle of fish.

The G-E alignment instructions are a little bit of a giveaway to this fact. They say the subcarrier reinsertion phase should be adjusted for maximum stereo separation at the higher audio frequencies, and the matrix (dimension) adjustment should be used for separation at the lower stereo frequencies. Put in simple terms, what this means is this: Having two variables, the subcarrier reinsertion phase and the dimension control, means that separation can be made high at two frequencies by what is really a "crooked" adjustment. Suitable choice of these frequencies means the separation does not get too high in between or beyond them (Fig. 7). But the very method means separation cannot be very high anywhere.

Fortunately there is a fairly simple remedy. A phase-linear low-pass filter is no problem, so we can use this to separate the L + R component. It is easy to null out the L + R component from the subcarrier detection, merely by returning the detector load circuit to the output point of the low-pass filter (Fig. 8). In this way, the whole L - R demodulation circuit "floats" at L + R audio, and a bandpass filter is not needed. Time delay can be equalized between L + R and L - R very completely by matching the delay caused by the detector load to that caused by the low-pass filter (Fig. 9). These are some of the things engineers have been finding out the hard way. What has hindered them, of course, has been the absence of any generator or test equipment to work with. The more successful manufacturers made their own rather than wait for a model to be made available by somebody else.

Posted June 6, 2024